#1 Your 200g cup of tea is boiling-hot. How much ice should you add to bring it down to a comfortable temperature of 65°C? Assume the ice is initially at -15°C. The specific heat of ice is 2.11 J/gK. #2 Geologists measure conductive heat flow out of the earth by drilling deep holes and measuring the temperature as a function of depth. Suppose that in a certain location the temperature increases by 20°C per kilometer of depth. What is the rate of heat conduction per square meter in this location? Assuming that this value is typical over all of earth’s surface, at approximately what rate is the earth losing heat via conduction? (The thermal conductivity of the rock is 2.5W/mK and the earth’s radius is 6400km.) #3 A black hole can be modeled as a perfect blackbody because it absorbs all incident light

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Unformatted text preview: and reflects nothing. A black hole of mass M has a total energy of Mc 2 , a surface area of 16G 2 M 2 /c 4 , and a temperature of hc 3 /16 2 kGM. G=6.67 10-11 m 3 / kg 1 s 2 , c=3.010 8 m/s , h=6.6310-34 Js , k=1.38 10-23 J/K , One solar-mass = 2 10 30 kg Calculate the total power radiated by a one-solar-mass black hole. Imagine that the black hole lives in vacuum where it emits radiation but absorbs nothing. As the black hole loses energy, its mass must decrease. Derive a differential equation for the mass as a function of time and solve the equation to obtain an expression for the lifetime of a black hole in terms of its initial mass. Calculate the lifetime of a one-solar-mass black hole and compare to the estimated age of the known universe (~10 10 years)....
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